From 64dad3622f9cfea1cf8c2662d2065d1b2000ebd9 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Tue, 18 Apr 2023 21:01:20 +0800 Subject: [PATCH] =?UTF-8?q?=E4=BF=AE=E6=94=B940504=E9=A2=98=E9=9D=A2?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具/latex界面修改题目内容.py | 2 +- 题库0.3/Problems.json | 5 +++-- 2 files changed, 4 insertions(+), 3 deletions(-) diff --git a/工具/latex界面修改题目内容.py b/工具/latex界面修改题目内容.py index b8793fd3..7a8af757 100644 --- a/工具/latex界面修改题目内容.py +++ b/工具/latex界面修改题目内容.py @@ -1,6 +1,6 @@ import os,re,json """这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭""" -problems = "40473,30499" +problems = "40504" editor = "王伟叶" def generate_number_set(string,dict): diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 5f36b388..3765eeee 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -470137,7 +470137,7 @@ }, "040504": { "id": "040504", - "content": "已知直线$l: y=-\\dfrac{1}{2} x$为双曲线$C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$)的一条渐近线, 且双曲线$C$经过点$(2 \\sqrt{2}, 1)$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.3]\n\\draw [->] (-10,0) -- (10,0) node [below] {$x$};\n\\draw [->] (0,-5) -- (0,5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [dashed] (10,5) -- (-10,-5) (10,-5) -- (-10,5);\n\\draw [domain = -10:{-2*sqrt(2)}, samples = 100] plot (\\x,{sqrt(\\x*\\x/4-2)});\n\\draw [domain = -10:{-2*sqrt(2)}, samples = 100] plot (\\x,{-sqrt(\\x*\\x/4-2)});\n\\draw [domain = {2*sqrt(2)}:10, samples = 100] plot (\\x,{sqrt(\\x*\\x/4-2)});\n\\draw [domain = {2*sqrt(2)}:10, samples = 100] plot (\\x,{-sqrt(\\x*\\x/4-2)}); \n\\end{tikzpicture}\n\\end{center}\n(1) 求双曲线$C$的方程;\\\\\n(2) 设直线$l: x=t y+4$与$C$交于$M, N$, 三角形$OMN$面积为$S$, 判断: 是否存在$t$使得$S=8 \\sqrt{15}$成立? 若存在, 求出$t$的值, 否则说明理由;\\\\\n(3) 设$A, B$是双曲线右支上两点, 若直线$l$上存在点$P$, 使得$\\triangle ABP$为正三角形, 求直线$AB$的斜率的取值范围.", + "content": "已知直线$l: y=-\\dfrac{1}{2} x$为双曲线$C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$)的一条渐近线, 且双曲线$C$经过点$(2 \\sqrt{2}, 1)$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.3]\n\\draw [->] (-10,0) -- (10,0) node [below] {$x$};\n\\draw [->] (0,-5) -- (0,5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [dashed] (10,5) -- (-10,-5) (10,-5) -- (-10,5);\n\\draw [domain = -10:{-2*sqrt(2)}, samples = 100] plot (\\x,{sqrt(\\x*\\x/4-2)});\n\\draw [domain = -10:{-2*sqrt(2)}, samples = 100] plot (\\x,{-sqrt(\\x*\\x/4-2)});\n\\draw [domain = {2*sqrt(2)}:10, samples = 100] plot (\\x,{sqrt(\\x*\\x/4-2)});\n\\draw [domain = {2*sqrt(2)}:10, samples = 100] plot (\\x,{-sqrt(\\x*\\x/4-2)}); \n\\end{tikzpicture}\n\\end{center}\n(1) 求双曲线$C$的方程;\\\\\n(2) 设直线$l': x=t y+4$与$C$交于$M, N$, 三角形$OMN$面积为$S$, 判断: 是否存在$t$使得$S=8 \\sqrt{15}$成立? 若存在, 求出$t$的值, 否则说明理由;\\\\\n(3) 设$A, B$是双曲线右支上两点, 若直线$l$上存在点$P$, 使得$\\triangle ABP$为正三角形, 求直线$AB$的斜率的取值范围.", "objs": [], "tags": [], "genre": "解答题", @@ -470147,7 +470147,8 @@ "usages": [], "origin": "23届交大附中模拟卷试题20", "edit": [ - "20230401\t王伟叶" + "20230401\t王伟叶", + "20230418\t王伟叶" ], "same": [], "related": [],